Data normalization

Initialization

We start the analysis by initializing the packages required for all the analysis performed in this section. We also define the root directory, within which all the input/output operations for this project will be performed. At the end of this document, a detailed software version information is provided for easier reproducibility of the analysis.

Normalization methodology

We use two different normalization strategy to answer specific questions -

  • For a given plate \(i\), the Cytoplasmic and Mitochondrial roGFP2 ratios are normalized by the median of all controls in the same plate i.e for cytoplasm - \[NormCyto(i) = \frac{Cyto_i} {median(Ctrl_i)}\] and for mitochondria, \[NormMito(i) = \frac{Mito_i} {median(Ctrl_i)}\]

This type of control based plate normalization will be suitable in comparing the redox levels in across organells and nutrients since the roGFP2 ratios has been commonly normalized to the plate control.

  • For a given plate \(i\) with the Cytoplasmic and Mitochondrial roGFP2 ratios \(j\) are normalized by their respective plate specific median roGFP2 ratios i.e for cytoplasm - \[NormCyto_{i} = \frac{Cyto_{ij} - median(Cyto_{i})} {mad(Cyto_{i})}\] and for mitochondria, \[NormMito_{i} = \frac{Mito_{ij} - median(Mito_{i})} {mad(Mito_{i})}\]

This type of organelle specific normalization will be suitable in comparing the redox levels in each organelle across all plates. Since this type of normalization tells us how far are the values from the plate median.

Furthermore, for each normalization strategy, we also summarized the quadruplicated values per gene by taking the median of the scaled values. Due to our outlier removal strategy in the previous section, many NA values were introduced. Each mutant has 4 values, we removed mutants with 2 or more NA values and those with only one NA value was substituted with the median of the other 3 observed values. Next, there were also multiple copies of the same mutants (genes) in either the same plate or different plates. We summarized them by taking the set of quadruplicated or median summarized values which have the maximum absolute median value.

Eventually, we generate the following -

  • A table with all the replicate values per organelle and nutrient conditions and the the median summarized value from all plates
  • A matrix with gene/mutants in rows and all combinations of organelle, nutrient and replicates (and median summarized value) in the column

Below is the table of cleaned raw data that we will use in our analysis.

rawDatCleaned = readRDS(paste0(path, "data/workspaces/YeastMutantRedox_RawDataCleaned.RDS"))
rawDatCleaned_ctrlfilt = readRDS(paste0(path, "data/workspaces/YeastMutantRedox_RawData_Outliers_and_PoorControlFiltered.RDS"))

normalizeScreenData = function(normMethod)
{
  
  if(normMethod == "fracControl"){
    normDat = split(rawDatCleaned_ctrlfilt, as.character(rawDatCleaned_ctrlfilt$Type))
    normDat = lapply(normDat, function(x) {
    split(x, x$Plate)})
  }
  
  if(normMethod == "robustZ"){
    normDat = split(rawDatCleaned, rawDatCleaned$Type)
    normDat = lapply(normDat, function(x) {
    split(x, x$Plate)})
  }
  
  normDatReps = normDat
  
  for (i in 1:length(normDat))
  {
    for (j in 1:length(normDat[[i]]))
    {
      tmp = droplevels(normDat[[i]][[j]])
      
      if(nrow(tmp) > 0) #since there are no entries from plate 150, was filtered in previous step
      {
        
      #---------------------------------------------------------------------------------------------
      # Separate Controls, Cytoplasam and Mitochondrial roGFP2 ratios per plate
      #---------------------------------------------------------------------------------------------
      
      # Control
      tmp.ctrl = droplevels(tmp[tmp$Content == "Control",])
      
      # Cytoplasm
      tmp.cyto = droplevels(tmp[tmp$Content == "Cytoplasm",])
      
      # Mitochondria
      tmp.mito = droplevels(tmp[tmp$Content == "Mitochondria",])
      
      rm(tmp)
      
      #---------------------------------------------------------------------------------------------
      # Compute the corresponding normalization factors (median & median absolute deviation)
      #---------------------------------------------------------------------------------------------
      
      # Normalizing factor - Control
      nf.ctrl.med = median(tmp.ctrl$roGFP2.ratio, na.rm = T)
      
      # Normalizing factor - Cytoplasm
      nf.cyto.med = median(tmp.cyto$roGFP2.ratio, na.rm = T)
      nf.cyto.mad = mad(tmp.cyto$roGFP2.ratio, na.rm = T)
      
      # Normalizing factor - Mitochondria
      nf.mito.med = median(tmp.mito$roGFP2.ratio, na.rm = T)
      nf.mito.mad = mad(tmp.mito$roGFP2.ratio, na.rm = T)
      
      #---------------------------------------------------------------------------------------------
      # The two normalization strategies (plate control and median based)
      #---------------------------------------------------------------------------------------------
      
      # Normalization 1 - Plate control based
      if (normMethod == "fracControl")
      {
        tmp.cyto$roGFP2.ratio = tmp.cyto$roGFP2.ratio / nf.ctrl.med
        tmp.mito$roGFP2.ratio = tmp.mito$roGFP2.ratio / nf.ctrl.med
      }
      
      # Normalization 2 - Plate median based
      if (normMethod == "robustZ")
      {
        tmp.cyto$roGFP2.ratio = (tmp.cyto$roGFP2.ratio - nf.cyto.med) / nf.cyto.mad
        tmp.mito$roGFP2.ratio = (tmp.mito$roGFP2.ratio - nf.mito.med) / nf.mito.mad
      }
      
      rm(nf.ctrl.med,
         nf.cyto.med,
         nf.cyto.mad,
         nf.mito.med,
         nf.mito.mad)
      
      #---------------------------------------------------------------------------------------------
      # Normalized data with replicates - coverting from long to wide table format
      #---------------------------------------------------------------------------------------------
      
      #---Cytoplasm---#
      
      tmp.cyto.repl = tmp.cyto %>%
        select(Gene.Symbol, Plate, Group, roGFP2.ratio, Type, Content) %>%
        group_by(Gene.Symbol, Group) %>%
        mutate(pseurep = paste0("roGFP2_ratio_", 1:n())) %>%
        spread(key = pseurep, value = roGFP2.ratio) %>%
        ungroup() %>%
        select(-Group) %>%
        rename(Genes = Gene.Symbol,
               Nutrient = Type,
               Organelle = Content)
      
      #---Mitochondria---#
      
      tmp.mito.repl = tmp.mito %>%
        select(Gene.Symbol, Plate, Group, roGFP2.ratio, Type, Content) %>%
        group_by(Gene.Symbol, Group) %>%
        mutate(pseurep = paste0("roGFP2_ratio_", 1:n())) %>%
        spread(key = pseurep, value = roGFP2.ratio) %>%
        ungroup() %>%
        select(-Group) %>%
        rename(Genes = Gene.Symbol,
               Nutrient = Type,
               Organelle = Content)
      
      #--Compilation---#
      
      normDatReps[[i]][[j]] = rbind(tmp.cyto.repl, tmp.mito.repl)
      
      #Deleting
      rm(tmp.ctrl,
         tmp.cyto,
         tmp.mito,
         tmp.cyto.repl,
         tmp.mito.repl)
      }
    }
   rm(j) 
  }
  rm(i)
 
  res = lapply(normDatReps, function(x) {
    x = do.call("rbind", x)
    x = as.data.frame(x)
    x$Plate     = factor(x$Plate)
    x$Organelle = factor(x$Organelle, levels = c("Mitochondria", "Cytoplasm"))
    x$Nutrient  = factor(x$Nutrient, levels = c("Glucose", "Galactose", "Glycerol"))
    rownames(x) = 1:nrow(x)
    return(x)
  })
  
  res = do.call("rbind", res)
  
  #-------------------------------------------------------------------------------------------------
  # Summarizing mutiple mutants (i.e same gene) from the same or different plates
  # Also dropping genes with 2 or more NA values
  # For genes with just 1 NA value, replacing it with the median of the remaining 3 observed values
  #-------------------------------------------------------------------------------------------------
  
  res = res %>%
    rowwise() %>%
    mutate(Median_roGFP2_ratio = median(c(roGFP2_ratio_1, roGFP2_ratio_2, roGFP2_ratio_3, roGFP2_ratio_4), na.rm=T),
           NA_per_row = sum(is.na(c(roGFP2_ratio_1, roGFP2_ratio_2, roGFP2_ratio_3, roGFP2_ratio_4)))) %>%
    filter(NA_per_row < 2) %>%
    ungroup() %>%
    mutate_at(vars(starts_with("roGFO2_ratio_")),
     function(x) ifelse(is.na(x), .$Median_roGFP2_ratio, x)) %>% 
    select(-NA_per_row) %>% 
    group_by(Organelle, Nutrient, Genes) %>% 
    top_n(n=1, abs(Median_roGFP2_ratio)) %>%
    ungroup()
  
  #-------------------------------------------------------------------------------------------------
  # Compiling all replicates across organelles and nutrient conditions into a single matrix
  #-------------------------------------------------------------------------------------------------
  
  redoxMat = data.table(res[,c("Genes", "Nutrient", "Organelle", "roGFP2_ratio_1", "roGFP2_ratio_2", "roGFP2_ratio_3", "roGFP2_ratio_4")])
  redoxMat = dcast(redoxMat, Genes ~ Organelle + Nutrient, fun.aggregate = function(x){x}, fill=NA,
              value.var = c("roGFP2_ratio_1", "roGFP2_ratio_2", "roGFP2_ratio_3", "roGFP2_ratio_4"))
  redoxMat = redoxMat[,c(1,
               2,8,14,20,
               3,9,15,21,
               4,10,16,22,
               5,11,17,23,
               6,12,18,24,
               7,13,19,25
               )]
  redoxMat = data.frame(redoxMat, stringsAsFactors = F )
  rownames(redoxMat) = redoxMat$Genes
  redoxMat = redoxMat[,-1]
  
  #-------------------------------------------------------------------------------------------------
  # Compiling the median values across organelles and nutrient conditions into a single matrix
  #-------------------------------------------------------------------------------------------------
  
  redoxMat_median = data.table(res[,c("Genes", "Nutrient", "Organelle", "Median_roGFP2_ratio")])
  redoxMat_median = dcast(redoxMat_median, Genes ~ Organelle + Nutrient, fun.aggregate = function(x){x}, fill=NA,
                    value.var = "Median_roGFP2_ratio")
  
  redoxMat_median = data.frame(redoxMat_median, stringsAsFactors = F )
  rownames(redoxMat_median) = redoxMat_median$Genes
  redoxMat_median = redoxMat_median[,-1]
  
  #-------------------------------------------------------------------------------------------------
  # Putting all the results into one
  #-------------------------------------------------------------------------------------------------
  
  res = list(redox_table = res, redox_replicates = redoxMat, redox_median = redoxMat_median)
  rm(normDat, normDatReps, redoxMat, redoxMat_median)
  return(res)
}

normDat.ctrNorm = normalizeScreenData(normMethod = "fracControl")
normDat.Znorm   = normalizeScreenData(normMethod = "robustZ")

Normalized data overview

We normalize the data as described above, below is the summary and the distribution of the normalized data -

  • For per plate normalization based on plate specific control
    Genes               Plate           Nutrient           Organelle   
 Length:4675        2      : 484   Glucose  :1561   Mitochondria:2336  
 Class :character   4      : 473   Galactose:1549   Cytoplasm   :2339  
 Mode  :character   3      : 472   Glycerol :1565                      
                    9      : 460                                       
                    8      : 418                                       
                    5      : 402                                       
                    (Other):1966                                       
 roGFP2_ratio_1     roGFP2_ratio_2     roGFP2_ratio_3     roGFP2_ratio_4    
 Min.   :0.000226   Min.   :0.000228   Min.   :0.000214   Min.   :0.000228  
 1st Qu.:1.199315   1st Qu.:1.197896   1st Qu.:1.204309   1st Qu.:1.197828  
 Median :1.611629   Median :1.606277   Median :1.598560   Median :1.595587  
 Mean   :1.627920   Mean   :1.625899   Mean   :1.623656   Mean   :1.623058  
 3rd Qu.:2.005188   3rd Qu.:2.000470   3rd Qu.:2.002525   3rd Qu.:2.011491  
 Max.   :4.213349   Max.   :4.139418   Max.   :3.748545   Max.   :4.145865  
                                                          NA's   :8         
 Median_roGFP2_ratio
 Min.   :0.000228   
 1st Qu.:1.202107   
 Median :1.606897   
 Mean   :1.627360   
 3rd Qu.:2.008029   
 Max.   :4.032744
  • For per plate normalization based on median organelle specific values
    Genes               Plate           Nutrient           Organelle   
 Length:4718        2      : 484   Glucose  :1573   Mitochondria:2358  
 Class :character   4      : 475   Galactose:1572   Cytoplasm   :2360  
 Mode  :character   3      : 472   Glycerol :1573                      
                    9      : 462                                       
                    8      : 420                                       
                    5      : 402                                       
                    (Other):2003                                       
 roGFP2_ratio_1       roGFP2_ratio_2       roGFP2_ratio_3      
 Min.   :-20.312549   Min.   :-20.399022   Min.   :-22.502049  
 1st Qu.: -0.683968   1st Qu.: -0.712392   1st Qu.: -0.676880  
 Median :  0.001691   Median :  0.000000   Median : -0.000439  
 Mean   :  0.006676   Mean   : -0.001119   Mean   : -0.010808  
 3rd Qu.:  0.659867   3rd Qu.:  0.675725   3rd Qu.:  0.650951  
 Max.   : 14.312598   Max.   : 13.803653   Max.   : 14.430594  
                                                               
 roGFP2_ratio_4       Median_roGFP2_ratio 
 Min.   :-15.909335   Min.   :-18.285617  
 1st Qu.: -0.701527   1st Qu.: -0.658868  
 Median : -0.001329   Median :  0.006156  
 Mean   : -0.013836   Mean   :  0.008269  
 3rd Qu.:  0.644119   3rd Qu.:  0.622557  
 Max.   : 13.349369   Max.   : 14.312598  
 NA's   :13
  • Number of mutants per condition
   GalactoseCytoplasm GalactoseMitochondria      GlucoseCytoplasm 
                  775                   774                   781 
  GlucoseMitochondria     GlycerolCytoplasm  GlycerolMitochondria 
                  780                   783                   782
  • Similarity between the normalization strategies
plotList = vector("list", 6)
names(plotList) = c("Glucose-Cytoplasm",   "Glucose-Mitochondria",
                    "Galactose-Cytoplasm", "Galactose-Mitochondria",
                    "Glycerol-Cytoplasm",  "Glycerol-Mitochondria")

plotListTop = plotList

for(i in c("Glucose", "Galactose", "Glycerol"))
{
  for(j in c("Cytoplasm", "Mitochondria"))
  {
    a = normDat.Znorm$redox_table[which(normDat.Znorm$redox_table$Nutrient == i & normDat.Znorm$redox_table$Organelle == j),]
    a = a[, c("Genes", "Median_roGFP2_ratio")]
    colnames(a) = c("Genes", "Znorm")
    
    b = normDat.ctrNorm$redox_table[which(normDat.ctrNorm$redox_table$Nutrient == i & normDat.ctrNorm$redox_table$Organelle == j),]
    b = b[, c("Genes", "Median_roGFP2_ratio")]
    colnames(b) = c("Genes", "Ctrlnorm")
    
    df = merge(a,b)
    
    topZ = quantile(df$Znorm, probs = c(0.05, 0.95))
    topC = quantile(df$Ctrlnorm, probs = c(0.05, 0.95))
    
    df_top = df[which(df$Znorm < topZ[1] | df$Znorm > topZ[2] | df$Ctrlnorm < topC[1] | df$Ctrlnorm > topC[2]),]
    
    id = paste(i,j,sep="-")
    
    plotList[[id]] = ggscatter(df, x = "Znorm", y = "Ctrlnorm",
                               color = "black", shape = 20, size = 0.5, # Points color, shape and size
                               add = "reg.line",  # Add regressin line
                               add.params = list(color = "blue", fill = "lightgray"), # Customize reg. line
                               conf.int = TRUE, # Add confidence interval
                               cor.coef = TRUE, # Add correlation coefficient. see ?stat_cor
                               cor.coeff.args = list(method = "spearman", label.x = -10, label.y = 1.5, label.sep = "\n"),
                               ggtheme = theme_classic(base_size = 8)) + labs(subtitle = id)
    
     plotListTop[[id]] = ggscatter(df_top, x = "Znorm", y = "Ctrlnorm",
                               color = "black", shape = 20, size = 0.5, # Points color, shape and size
                               add = "reg.line",  # Add regressin line
                               add.params = list(color = "blue", fill = "lightgray"), # Customize reg. line
                               conf.int = TRUE, # Add confidence interval
                               cor.coef = TRUE, # Add correlation coefficient. see ?stat_cor
                               cor.coeff.args = list(method = "spearman",  label.x = -10, label.y = 1.5, label.sep = "\n"),
                               ggtheme = theme_classic(base_size = 8)) + labs(subtitle = id)
    
    
    rm(a, b, df,df_top, topZ, topC, id)
  }
  rm(j)
}
rm(i)

Plotting the correlation between the two normalization techniques for all matching mutants

Plotting the correlation between the two normalization techniques using ONLY the top hits 5% (high/low) roGFP2 ratios from either normalization method

Sample similarity - Dimensionality reduction

Next, we apply the dimensionality reduction method Multidimesional scaling (MDS) on the roGFP2 ratio values normalized by the plate control and Robust Z normalized to identify the major grouping of the yeast mutants based on their redox status across organelle and nutrient conditions. We distinctly see that the redox status is different between the organelles (also seen by density plots, higher in mitochondria compared to cytoplasm) and within the organelles the mutants group by the nutrient conditions.

getMDSdata = function(dat) {
    mds = cmdscale(dist(t(dat)), eig = TRUE, k = 2)$points
    colnames(mds) = c("MDS1", "MDS2")
    
    col_anno = do.call("rbind", strsplit(rownames(mds), "_"))
    col_anno = col_anno[, -c(1:3)]
    colnames(col_anno) = c("Compartment", "Nutrient")
    mds = data.frame(mds, col_anno)
}

mdsZ = getMDSdata(dat = normDat.Znorm$redox_replicates)
mdsC = getMDSdata(dat = normDat.ctrNorm$redox_replicates)

p1 = ggplot(mdsZ, aes(x = MDS1, y = MDS2)) + theme_classic(base_size = 8) + labs(subtitle = "Robust Z normalized") + 
    geom_point(aes(color = Nutrient, shape = Compartment), size = 2) + scale_color_manual(values = c("#fc8d62", 
    "#66c2a5", "#8da0cb"))

p2 = ggplot(mdsC, aes(x = MDS1, y = MDS2)) + theme_classic(base_size = 8) + labs(subtitle = "Plate control normalized") + 
    geom_point(aes(color = Nutrient, shape = Compartment), size = 2) + scale_color_manual(values = c("#fc8d62", 
    "#66c2a5", "#8da0cb"))

pA = p1 + p2 + plot_layout(guides = "collect")

p3 <- ggviolin(normDat.Znorm$redox_table, x = "Organelle", y = "Median_roGFP2_ratio", 
    xlab = "", ylab = "Median roGFP2 ratio", draw_quantiles = 0.5, fill = "Organelle", 
    facet.by = "Nutrient", color = "grey90") + stat_compare_means(label = "p.format", 
    method = "wilcox", cex = 2) + labs(subtitle = "Robust Z normalized") + theme_classic(base_size = 8) + 
    theme(legend.position = "right", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + 
    scale_fill_manual(values = c("#b2df8a", "#7570b3"))


p4 <- ggviolin(normDat.ctrNorm$redox_table, x = "Organelle", y = "Median_roGFP2_ratio", 
    xlab = "", ylab = "Median roGFP2 ratio", draw_quantiles = 0.5, fill = "Organelle", 
    facet.by = "Nutrient", color = "grey90") + stat_compare_means(label = "p.format", 
    method = "wilcox", cex = 2) + labs(subtitle = "Plate control normalized") + theme_classic(base_size = 8) + 
    theme(legend.position = "right", axis.text.x = element_blank(), axis.ticks.x = element_blank()) + 
    scale_fill_manual(values = c("#b2df8a", "#7570b3"))

pB = p3 + p4 + plot_layout(guides = "collect")

p5 = ggviolin(normDat.Znorm$redox_table, x = "Nutrient", y = "Median_roGFP2_ratio", 
    xlab = "", ylab = "Median roGFP2 ratio", draw_quantiles = 0.5, fill = "Nutrient", 
    facet.by = "Organelle", color = "grey90") + stat_compare_means(method = "anova", 
    label.y = 22, label.x = 1.5, cex = 2) + stat_compare_means(label = "p.signif", 
    method = "wilcox", ref.group = ".all.", hide.ns = TRUE) + scale_fill_manual(values = c("#66c2a5", 
    "#fc8d62", "#8da0cb")) + labs(subtitle = "Robust Z normalized") + theme_classic(base_size = 8) + 
    theme(legend.position = "right", axis.text.x = element_blank(), axis.ticks.x = element_blank())

p6 = ggviolin(normDat.ctrNorm$redox_table, x = "Nutrient", y = "Median_roGFP2_ratio", 
    xlab = "", ylab = "Median roGFP2 ratio", draw_quantiles = 0.5, fill = "Nutrient", 
    facet.by = "Organelle", color = "grey90") + stat_compare_means(method = "anova", 
    label.y = 5, label.x = 1.5, cex = 2) + stat_compare_means(label = "p.signif", 
    method = "wilcox", ref.group = ".all.", hide.ns = TRUE) + scale_fill_manual(values = c("#66c2a5", 
    "#fc8d62", "#8da0cb")) + labs(subtitle = "Plate control normalized") + theme_classic(base_size = 8) + 
    theme(legend.position = "right", axis.text.x = element_blank(), axis.ticks.x = element_blank())

pC = p5 + p6 + plot_layout(guides = "collect")

p = pA/pB/pC

ggsave(filename = paste0(path, "analysis/normalization/roGFP2_ratio_comparison_nutrient_compartments.pdf"), 
    plot = p, width = 7, height = 7)

p

Replicate similarity - Correlation

Below we show the correlation among replicates.

  • first with plate median (nutrient specific) based Robust Z normalization

  • second with control based normalization

Distribution of normalized data

  • For per plate normalization based on plate specific control and an interactive data table to access the data

  • For per plate normalization based on median organelle specific values and an interactive data table to access the data

Session information

R version 3.6.2 (2019-12-12)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.16

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] RColorBrewer_1.1-2 pheatmap_1.0.12    patchwork_1.0.0    ggpubr_0.2.4      
 [5] magrittr_1.5       ggrepel_0.8.1      WriteXLS_5.0.0     data.table_1.12.8 
 [9] forcats_0.4.0      stringr_1.4.0      dplyr_0.8.4        purrr_0.3.3       
[13] readr_1.3.1        tidyr_1.0.2        tibble_2.1.3       ggplot2_3.2.1     
[17] tidyverse_1.3.0    DT_0.12            rmdformats_0.3.6   knitr_1.28        

loaded via a namespace (and not attached):
 [1] httr_1.4.1        jsonlite_1.6.1    modelr_0.1.5      shiny_1.4.0      
 [5] assertthat_0.2.1  cellranger_1.1.0  yaml_2.2.1        pillar_1.4.3     
 [9] backports_1.1.5   lattice_0.20-38   glue_1.3.1        digest_0.6.23    
[13] promises_1.1.0    ggsignif_0.6.0    rvest_0.3.5       colorspace_1.4-1 
[17] htmltools_0.4.0   httpuv_1.5.5      plyr_1.8.5        pkgconfig_2.0.3  
[21] broom_0.5.4       haven_2.2.0       bookdown_0.17     xtable_1.8-4     
[25] scales_1.1.0      later_1.0.0       generics_0.0.2    farver_2.0.3     
[29] ellipsis_0.3.0    withr_2.1.2       lazyeval_0.2.2    cli_2.0.1        
[33] mime_0.9          crayon_1.3.4      readxl_1.3.1      evaluate_0.14    
[37] fs_1.3.1          fansi_0.4.1       nlme_3.1-144      xml2_1.2.2       
[41] tools_3.6.2       hms_0.5.3         formatR_1.7       lifecycle_0.1.0  
[45] munsell_0.5.0     reprex_0.3.0      compiler_3.6.2    rlang_0.4.4      
[49] grid_3.6.2        rstudioapi_0.11   htmlwidgets_1.5.1 crosstalk_1.0.0  
[53] labeling_0.3      rmarkdown_2.1     gtable_0.3.0      DBI_1.1.0        
[57] reshape2_1.4.3    R6_2.4.1          lubridate_1.7.4   fastmap_1.0.1    
[61] stringi_1.4.5     Rcpp_1.0.3        vctrs_0.2.2       dbplyr_1.4.2     
[65] tidyselect_1.0.0  xfun_0.12

Ashwini Kumar Sharma, PhD

2021-06-11